Biomedical Engineering Reference
In-Depth Information
similar to their equation (1.33) may be obtained by combining the two-energy
equations (1.25) and (1.26) in the present model as
ρc
∂T
t
∂t
∂
∂x
j
f
+
ρ
f
c
pf
u
j
T
εk
f
∂
+(1
f
s
f
∂
∂x
j
T
ε
)
k
s
∂
T
∂
T
=
+(1
−
+
εk
dis
jk
−
ε
)
S
m
∂x
j
∂x
j
∂x
k
(1.35)
When the three temperature gradients on the right-hand side are close and
εk
dis
jk
=
k
p
δ
jk
, the foregoing equation reduces to
ρc
∂T
t
∂t
∂
∂x
j
f
+
ρ
f
c
p
f
u
j
T
(
εk
f
+(1
+(1
(1.36)
∂
∂x
j
ε
)
k
s
)
∂T
t
∂x
j
+
k
p
∂T
t
=
−
− ε
)
S
m
∂x
j
which is close to the equation of Chen and Holmes, except that
ρ
f
c
p
f
ω
j
(
T
a
−
T
t
) is missing, as in the models of Wulff and Klinger, since it should
vanish, as we add equations (1.25) and (1.26).
1.5 Three-Energy Equation Model for Countercurrent
Heat Transfer in a Circulatory System
1.5.1 Related Work
Bazett and his colleagues (1948a,b) conducted a series of experimental studies
on countercurrent heat exchange in the circulatory system. They found that
the axial temperature gradient in the limb artery of human, under conditions
of very low ambient temperature, is an order of magnitude higher than that
under normal ambient conditions. From these experimental observations, they
proposed the concept of venous shunting to the periphery, namely, that the
countercurrent heat transfer takes place in the deep vasculature at the same
time the blood is directed to the cutaneous circulation in close proximity to the
surroundings. Their experimental finding brought attention to the important
role of countercurrent heat exchange in bioheat transfer. Especially when the
anatomical configuration of the main supply artery and vein in the limbs
is treated, the effect of countercurrent heat transfer between closely spaced
arteries and veins in the tissue must be taken into full consideration.
Following the experimental studies conducted by Bazett and his colleagues
(1948a,b), Scholander and Krog (1957), and Mitchell and Myers (1968) inves-
tigated such an effect and successfully demonstrated that the countercurrent
heat exchange reduces heat loss from the extremity to the surroundings, which
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